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Modelling and simulation of hydrodynamics in double loop circulating ﬂuidizedbed reactor for chemical looping combustion process Yuanwei Zhang a, * , Zhongxi Chao b , Hugo A. Jakobsen a a b

Department of Chemical Engineering, Norwegian University of Science and Technology, Sem Sælandsvei 4, Trondheim 7034, Norway Safetec Nordic AS, Klæbuveien 194, Trondheim 7037, Norway

A R T I C L E

I N F O

Article history: Received 25 July 2016 Received in revised form 31 October 2016 Accepted 6 January 2017 Available online 9 January 2017 Keywords: Double loop circulating ﬂuidized bed CFD model for circulating ﬂuidized bed Kinetic theory of granular ﬂow Hydrodynamics

A B S T R A C T A multiphase CFD model has been developed and implemented in an in-house code for a coupled double loop circulation ﬂuidized bed (DLCFB) reactor which can be utilized for the chemical looping combustion process. The air reactor and the fuel reactor were operated in fast ﬂuidization regime and simulated separately, the connection between the two reactors is realized through speciﬁc inlet and outlet boundary conditions. This work represents a ﬁrst attempt to model and simulate the novel DLCFB system. The model predictions of the axial pressure proﬁles are in good agreement with the experimental data reported in the literatures. In addition, typical core-annulus structure of radial solid volume fraction distribution can be well predicted in both reactors. These indicate the capability of the model for predicting the cold ﬂow performance of the DLCFB system. Furthermore, the effects of superﬁcial gas velocity, total solid inventory on the ﬂow characteristics have been examined. The results show that an increase of the gas velocity could enhance the solid exchanges between the two reactors. The additional solids were accumulated in the bottom of the reactors when the total solid inventory was increased. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Over the past decades, global warming has caused signiﬁcant negative impacts on the natural and human system. There is an overwhelming consensus among scientists that the anthropogenic emissions of carbon dioxide (CO2 ) are the major contributor to the warming trend. That is why a tremendous number of technologies have been advocated to reduce the CO2 emission, especially from the energy sector. Carbon Capture and Storage (CCS) is a promising technology for reducing CO2 emissions because of the increasing fossil fuel consumption and the domination of carbon-intensive industries [1]. The CCS technology can be divided into four groups as pre-combustion, oxy-fuel combustion, post-combustion and chemical looping combustion (CLC). Since the ﬁrst three ones will result in a drop in process eﬃciency and high energy penalty [2], CLC has drawn more and more attention. CLC is a novel combustion process with two successive reaction systems forming a chemical loop instead of the conventional

* Corresponding author. E-mail address: [email protected] (Y. Zhang).

http://dx.doi.org/10.1016/j.powtec.2017.01.028 0032-5910/© 2017 Elsevier B.V. All rights reserved.

combustion reaction system. The process primarily consists of two ﬂuidized bed reactors, the fuel reactor (FR) and the air reactor (AR). In the FR, the fuel reacts with the metal oxide which is called an oxygen carrier (OC) to produce CO2 and H2 O • H2 O can then be removed by condensation and only carbon dioxide is remaining for storage. The oxygen carrier is being reduced from MeOa to MeOa −1 and transported to the AR. In the AR the MeOa −1 oxidized to MeOa by oxygen of the air and circulating back to FR. In this way, the mixing of fuel and air is avoided and CO2 will inherently not be diluted with nitrogen which would otherwise require high energy cost. More detailed descriptions of the development of the CLC process can be found in several review articles [2–4]. In recent years computational ﬂuid dynamics (CFD) has become a useful tool for studying the ﬂuidized bed system. There are two modelling frameworks for modelling the gas-solid ﬂow, the EulerianLagrangian (E-L) model and the Eulerian-Eulerian model, also known as the two-ﬂuid model. Due to the high computational resources required for solving the E-L model, most researches choose the twoﬂuid model for studying the ﬂuidized bed reactor. In this method, which is also used in this work, both phases are described as interpenetrating continua and modelled in the framework of the Navier-Stokes equations using averaging quantities. CFD simulations by use of the two-ﬂuid model for describing the CLC process have been employed in several articles. The ﬁrst

36

Y. Zhang et al. / Powder Technology 310 (2017) 35–45 Table 1 Empirical parameters for the j-e model [22]. Cl

s0

se

C1

C2

Cb

0.09

1.00

1.30

1.44

1.92

0.25

authors have also carried out the full loop simulation of the CLC process. Kruggel-Emden et al. [11] applied the exchanges of solid mass through a time-dependent inlet and outlet boundary coupled to the fuel and air reactors, the developed interconnected CFD model shows promising results for developments of the CLC process. Wang et al. [12] and Bougamra and Huilin [13]studied the CLC process by developing a 2D full loop CFD model and successfully predicted the hydrodynamic characteristics. Besides the 2D models, 3D models have also employed by Guan et al. [14] and Geng et al. [15] for hydrodynamic studies. Up to date, most experimental and numerical studies [5-11,13-15] were performed on a typical conﬁguration which consists of a high velocity riser as the AR and a low velocity bubbling

Fig. 1. (a) Sketch of the double loop circulating ﬂuidized bed reactor [18]. (b) Schematic of the 2D computational domain.

attempt was made by Jung and Gamwo [5] followed by Deng et al. [6,7] and Jin et al. [8] In their simulations, the typical bubble behaviour and ﬂow patten were observed but no experimental data were available for the model validation. Moreover low fuel gas conversions were predicted due to the bubbles formed and the reacting gas bypassing the solid inside the bubbling bed. KruggelEmden et al. [9], Mahalatkar et al. [10] also conducted studies of the reactive performance of the CLC system. The simulation studies mentioned above were limited to the fuel reactor only, but a few

Fig. 2. Comparison of pressure proﬁles along the height of the FR and the AR with different grid numbers.

Y. Zhang et al. / Powder Technology 310 (2017) 35–45

37

Table 2 Main geometric and operating parameters for DLCFB [18]. Description Reactor geometry AR height AR diameter FR height FR diameter Particle properties Mean particle size Particle density Operational condition Operating pressure Operating temperature Gas superﬁcial velocity of AR Gas superﬁcial velocity of FR

Unit

Value

m m m m

5 0.23 5 0.144

lm kg/m3

50 7000

atm K m/s m/s

1.0 293 2.1–2.6 1.8–3.2

ﬂuidized bed as the FR. Only a few attempts [12,16,17] were made for other reactor designs. In order to get suﬃciently high solid circulation rate and fuel conversion, enhance gas-solid contact and realize ﬂexible operation, SINTEF Energy Research and the Norwegian University of Science and Technology have designed a double loop circulating ﬂuidized bed (DLCFB) reactor for CLC process [18]. This system is modelled and simulated in this work. In their DLCFB system, which is sketched in Fig. 1 (a), the air reactor as well as the fuel reactor were operated as a circulating ﬂuidized bed reactor. The interconnection between the reactor units was realized by means of two divided loop-seals and a bottom extraction/lift. The loopseals are ﬂuidized through three bubble caps (central, external and internal) so that the solids entrained by one reactor can be lead into the other reactor or re-circulated back into the original one. During the experiment, the solid outﬂow from one reactor is injected into the bottom of the other reactor through the cyclones and external loop-seals. Proper understanding of the complex gas-solid hydrodynamic characteristics of the DLCFB reactor is required for providing guidance in the design and operation of the CLC reactor system. In the present work, a multiphase CFD model for an interconnected DLCFB reactor has been developed and implemented using the Fortran programming language. The main objective of this investigation is to validate the model and to explore the hydrodynamic behaviours of the system under different operational conditions. 2. Multiphase ﬂuid dynamics model This section presents the governing equations for each phase as well as the constitutive closure models. For the gas phase, the transport equations can be derived by applying a suitable averaging procedure to the local instantaneous equations [19], while the transport

Table 3 Main geometric and operating parameters for CFB [33]. Description Reactor geometry CFB riser height CFB riser diameter Particle properties Mean particle size Particle density Operational condition Operating pressure Operating temperature Gas superﬁcial velocity of inlet

Unit

Value

m m

6.6 0.075

lm kg/m3

75 1654

atm K m/s

1.0 293 2.61

Fig. 3. Comparison of the radial distribution of solid volume fraction between simulation and experiment results. (a) z=1.86m; (b) z=4.18m; (c) z=5.52m.

equations for solid phase originate from the ensemble average of a single-particle quantity over the Boltzmann integral-differential equation [20].

38

Y. Zhang et al. / Powder Technology 310 (2017) 35–45 Table 4 simulation parameters. Description

Unit

Value

Grid size Gas viscosity Gas density Sphericity of particle Restitution coeﬃcient of particles Time step

– kg m −1 s −1 kg/m3 – – s

0.0048 × 0.02 m 1.82 × 10 −5 1.2 1 0.99 1.0 × 10 −4

2.1. Continuity equations The continuity equations for the gas phase and solid phase are given as follows:

∂ (a q ) + ∇ • (ag qg v g ) = 0 ∂t g g ∂ (a q ) + ∇ • (as qs v s ) = 0 ∂t s s

(1) (2)

The volume fraction of gas phase (a g ) and solid phase (a s ) are sum up to one in the two-phase model: ag + as = 1

(3)

2.2. momentum equations The momentum equations for the gas and solid phases can be expressed by

∂ g + ag qg g (4) (a q v ) + ∇ • (ag qg v g v g ) = −ag ∇p − ∇ • ag t¯¯ g + M ∂t g g g ∂ s + as qs g (a q v ) + ∇ • (as qs v s v s ) = −as ∇p − ∇ • as t¯¯ s + M (5) ∂t s s s 2.3. Turbulence model for the gas phase A standard j-e turbulence model [21,22] has been used to describe the turbulence phenomena in the gas phase, the gas turbulent kinetic energy equation is expressed by

∂ (a q k ) + ∇ • (ag qg kg v g ) = ag (−t¯¯ t : ∇ v g + St ) ∂t g g g +∇ •

ag

l g,t ∇kg − ag qg eg sg

(6)

The turbulent energy dissipation rate equation is formulated as eg ¯ ∂ (ag qg eg ) + ∇ • (ag qg eg v g ) = ag C1 −t¯ t : ∇ v g + St kg ∂t

+∇ •

ag

eg2 l g,t ∇eg − a g qg C2 se kg

(7)

2.4. Constitutive closure models 2.4.1. Inter-phase drag model The two phases are coupled through the interfacial momentum transfer, which is dominated by the drag force. In this study, the Gibilaro [23] drag model was used. The cluster effect inside the riser is modelled by use of the method proposed by McKeen and Pugsley [24]. The interfacial drag force is thus modelled as Fig. 4. Comparison of the axial solid velocity between simulation and experiment results. (a) z=1.86m; (b) z=4.18m; (c) z=5.52m.

g = −M s = C FD = Cb (v s − v g ) M

(8)

The value of the calibration parameter C is different for different kinds of particles. It is used as a tuning parameter to match the

Y. Zhang et al. / Powder Technology 310 (2017) 35–45

simulation results with the experimental pressure and solid volume fraction data. For the particle used in the DLCFB reactor system, the value C is 0.4. The friction factor is given by [23] b=

17.3 Rep + 0.336

qg v s − v g as ag−1.8 dp

(9)

s g − u dp ag qg u lg

the ﬂuctuating kinetic energy of the particles, was introduced and can be expressed as 3 2

The conductivity of the granular temperature is calculated from [27] (10)

2 6 15 l dilute Hs s 2 (16) 1 + as g0 (1 + e) +2as qs dp (1+e)g0 js = 2 (1 + e)g0 5 p

2.4.2. Closure model for the gas phase The gas phase viscous stress tensor in Eq. (4) is given as t¯¯ g = −l g

The collisional energy dissipation term is given by [28]

2 ∇ v g + (∇ v g )T − (∇ • v g )¯¯I 3

(11)

in which the bulk viscosity of the continuous gas was set to zero. In the turbulence model, turbulent viscosity is deﬁned by l g,t = qg Cl

k2g

(12)

eg

∂ (a q H ) + ∇ • (as qs Hi v s ) = −t¯¯ s : ∇ v s +∇ • (js ∇Hs )−3bHs −cs ∂t s s s (15)

where the particle Reynolds number is Rep =

39

cs = 3(1 − e2 )as2 qs g0 Hs

4 dp

Hs − ∇ • v s p

(17)

The radial distribution function denote the average distance between particles and is calculated from an empirical relation [29] g0 =

1 + 2.5as + 4.5904as2 + 4.515439as3 3 0.67802 s 1 − aamax

(18)

s

The turbulent kinetic energy production St due to the motion of the particles can be modelled with the method proposed by [25] St = Cb b(v s − v g )2

(13)

The turbulent stress tensor is modelled by using the gradient- and Boussinesq hypotheses [22]: 2 t¯¯ t = − qg kg ¯¯I + l g,t 3

2 ∇ v g + (∇ v g )T − (∇ • v g ) ¯¯I 3

The total pressure tensor of the solid phase occurring in Eqs. (5) and (15) is modelled similar to the Newton’s viscosity law: 2 t¯¯ s = − (−ps + as l B,s ∇ • v s ) − as l s ∇ v s + (∇ v s )T − (∇ • v s )¯¯I 3

(19)

where the solid pressure ps and the bulk viscosity l B,s is taken from [30]

(14)

The empirical parameters in the j-e turbulence model are given in Table 1. 2.4.3. Kinetic theory of granular ﬂow When the solid phase is treated as a ﬂuid in the two-ﬂuid model, some physical properties like solid pressure, solid viscosity are missing. The kinetic theory of granular ﬂow (KTGF) [26] was used to derive the different physical properties of the solid phase. In this method, the granular temperature, which is a statistical measure of

ps = a s qs Hs [1 + 2(1 − e)a s g0 ]

l B,s

4 4 Hs + as qs dp g0 (1 + e) = as qs dp g0 (1 + e) 3 p 5

(20)

(21)

The solid phase shear viscosity can be modelled following the approach by [27] ls =

2 4 2l dilute 4 Hs s 1 + a s g0 (1 + e) + a s qs g0 (1 + e) as g0 (1 + e) 5 5 p

Fig. 5. Comparison of pressure proﬁles in FR between simulation and experiment results.

(22)

40

Y. Zhang et al. / Powder Technology 310 (2017) 35–45

Fig. 6. Comparison of pressure proﬁles in AR between simulation and experiment results.

in which the dilute viscosity l dilute is expressed by s l dilute = s

5 qs dp pHs 96

(23)

order to keep the mass balance inside one reactor. In this way, a full loop was fulﬁlled for one time step. Then, another computation loop for next time step will run repeatedly. 3.3. Initial and boundary conditions

3. Interconnected model and numerical considerations 3.1. Geometry of the reactors and the deﬁnition of the computational domain In the DLCFB system, the air reactor as well as the fuel reactor are operated in the fast ﬂuidization regime in order to raise the fuel conversion with a better gas-solid contact of the upper part of the rector. Both reactors are 5 m high while the diameter of AR and FR are 0.23 m and 0.144 m, respectively. The graphical representation of this architecture can be found in [18]. The 2D plane geometry was chosen for the simulation of the two reactors, which is sketched in Fig. 1 (b), having the same dimensions as the experimental setup. The computational domain was meshed by using uniform grids in each direction. Three different grid sizes (0.006 × 0.027 m, 0.0048 × 0.02 m, 0.004 × 0.016 m) were examined. The corresponding results are shown in Fig. 2. It can be seen that the pressure proﬁle predicted by the coarse grid is somewhat higher than the other two in the lower part of the reactors. However, overall no obvious differences are observed comparing the results for the three grid sizes. Considering the simulation time and the numerical accuracy, the medium grid (0.0048 × 0.02 m) was used in this study.

Initially, there is no gas ﬂow in the reactor and the bed is at rest with a particle volume fraction of 0.6. A uniform gas plug ﬂow is applied at the inlets of the reactors, the inlet solid ﬂux of one of the reactors was kept consistent with the outlet solid ﬂux of the other one with a prescribed solid volume fraction at the inlet. The normal velocities at all boundaries are set to zero. The no-slip wall boundary condition was set for the gas phase while the solids were allowed to slip along the wall, following the Eq. (24) from [22].

v s,z |wall =

dp ∂ v s,z 1/3 ∂ r

(24)

as

where v s,z is the axial velocity of the particles. r indicates the radial direction.

5

Fuel reactor Air reactor

4.5 4

3.2. Combination of two reactors

Superficial velocity

Two different sets of coordinates and parameters were adopted to solve the governing equations for the AR and the FR, respectively. The solid ﬂowing out of the AR is fed into the bottom of the FR, and in the similar way all the solids that exited at the outlet of FR will be injected into the bottom of the AR. The exchange of the solid ﬂow between the reactor units were realized through the time-dependent inlet and outlet boundary conditions. At each simulation time step, the processes in the two risers were simulated separately, the solid ﬂux of the inlet of one riser was calculated from the solid ﬂowing out of the outlet of the other riser. In the experimental rig, this kind of continuous solid exchange is achieved by means of cyclones and divided loop-seals. The cyclones are neglected in the simulation by assuming the eﬃciency of cyclone is equal to one. The bottom extraction/lift is replaced by an internal recirculation mechanism in

Reactor height [m]

3.5

FR: 2.6 m/s AR: 2.4 m/s

3 2.5 2 1.5 1 0.5 0

0

0.05

0.1

0.15

Solid volume fraction [−] Fig. 7. Axial proﬁle of time-averaged solids volume fraction.

0.2

Y. Zhang et al. / Powder Technology 310 (2017) 35–45

0.3

41

0.04

8

10

Solid volume fraction at z/HFR=0.1 0.035

Solid axial velocity at z/H =0.1 FR

0.25

8

Solid volume fraction at z/HFR=0.5

6

Solid volume fraction at z/H =0.74

0.03

6

FR

2

0.1

0

0.05

−2

0 −1

−0.8

−0.6

−0.4 −0.2 0 0.2 0.4 Normalized radial position [−]

0.6

0.8

1

FR

2

0.015

0

0.01

−2

0.005

−4

−0.8

−0.6

−0.4 −0.2 0 0.2 0.4 Normalized radial position [−]

(a)

0.6

0.8

1

−6

(b)

0.5

0.03

12

Solid volume fraction at z/HAR=0.1

0.45

4

FR

0.02

0 −1

−4

Solid axial velocity at z/H =0.74

0.025

Solid axial velocity [m/s]

0.15

Solid volume fraction [−]

4

Solid axial velocity [m/s]

Solid volume fraction [−]

Solid axial velocity at z/H =0.5 0.2

8

10

Solid axial velocity at z/HAR=0.1

0.025

0.4

6

Solid volume fraction at z/HAR=0.5

8

Solid volume fraction at z/H =0.74

4

0.25

2

0.2

0

0.15

−2

0.1

−4

0.05

−6

0 −1

−0.8

−0.6

−0.4 −0.2 0 0.2 0.4 Normalized radial position [−]

0.6

0.8

1

−8

Solid axial velocity at z/HAR=0.5

0.02

4

Solid axial velocity at z/HAR=0.74 0.015

2

0.01

0

0.005

−2

0 −1

−0.8

−0.6

−0.4 −0.2 0 0.2 0.4 Normalized radial position [−]

(c)

0.6

0.8

1

Solid axial velocity [m/s]

0.3

Solid volume fraction [−]

6 Solid axial velocity [m/s]

Solid volume fraction [−]

AR

0.35

−4

(d)

Fig. 8. Radial distribution of solid volume fraction and axial solid velocity of the FR (a, b) and AR (c, d) (conditions: UFR = 2.6, UAR = 2.4).

For all scalar variables but pressure, Dirichlet boundary conditions are used at the inlet, while Neumann conditions are used at the other boundaries. For the pressure correction equations, all the boundaries except outlet were adopted Neumann conditions. At the outlet a ﬁxed pressure is speciﬁed.

3.4. Numerical procedure The two-ﬂuid model equations were discretized by the ﬁnite volume method and implemented in an in-house code. The algorithm is based on the work by Lindborg [21] and Jakobsen [22]. The second order central differential scheme was used to discretize the diffusion terms. In order to reduce the oscillation and keep higher-order accuracy of the numerical solution, a total variation diminishing (TVD) scheme was employed for discretizing the convention term [31,32]. In this scheme, cell face values are calculated from the combination of upwind scheme part and a central difference anti-diffusive part, which controlled by a smoothness function. In this way, a higherorder discretization scheme is used in smooth regions and reduce to the ﬁrst order at local extrema of the solution. The upwind part is

treated fully implicitly while the anti-diffusive part is treated explicitly. The SIMPLE algorithm for multiphase ﬂow is selected for the pressure-velocity coupling [21,22]. Due to the strong coupling of the two phases, the coupling terms are singled out from the discretized transport equations, and then the coupled equations are solved simultaneously by using a coupled solver. All the linear equation systems are solved by the preconditioned bi-conjugate gradient (BCG) algorithm.

4. Results and discussion 4.1. Model validation For validating the interconnected model for the CLC process, the reported experimental data from Bischi et al. [18] was used. But in their experiments, only axial pressures along the reactors were measured. In order to characterize the capabilities of the model, another set of experimental data from another CFB system documented by Miller and Gidaspow [33] is simulated to test the hydrodynamic behaviours of a single riser. Details of the experimental conditions

42

Y. Zhang et al. / Powder Technology 310 (2017) 35–45 5

U

FR

5

= 1.8 m/s

UFR = 1.8 m/s

UFR = 2.1 m/s

4.5

U

FR

4.5

= 2.4 m/s

= 2.4 m/s

FR

4

3.5 AR

3.5

= 2.6 m/s

UAR = 2.6 m/s Reactor height [m]

U Reactor height [m]

= 2.1 m/s

U

FR

4

3

Fuel reactor

2.5

2

1.5

3

2

Zoom in

1

1

0.5

0.5

0

0.05

0.1

0.15

Air reactor

2.5

1.5

Zoom in

0

U

0.2

0.25

0.3

0.35

0

0

0.05

0.1

0.15

Solid volume fraction [−]

Solid volume fraction [−]

(a)

(b)

0.2

0.25

Fig. 9. Effect of superﬁcial gas velocity in FR on the solid volume fraction along the height of both reactors.

4.1.1. Validation for single CFB model The governing equations used in the single riser model are the same as those used for the coupled CFB model developed above except the calibration parameter C in drag force model is 0.3. That is because the particle used for the single CFB model validation is different with the one used in the DLCFB model. The calibration parameter value can be adjusted and determined by comparing the calculated results with the experimental axial pressure drop and radial solid volume fraction data. Once the value C is determined for one kind of particle, the parameter is ﬁxed for the simulations with different operation conditions. The entry mass ﬂux of the particles are set equal to the mass ﬂux at the outlet to ensure all particles leaving the riser could be circulated back to the system. Fig. 3 shows the calculated radial proﬁles of solid volume fraction and their comparison with experimental data. Three riser sections, at 1.86 m, 4.18 m, and 5.52 m above the ﬂow distributor, have been investigated. At 1.86 m above the inlet, Miller and Gidaspow [33] reported that the riser is closely packed in a bubbling ﬂow situation. Since the different inlet conditions between the experimental and calculated situation, it is reasonable to believe that there might be some discrepancies at the lowest section. When the height reaches 4.18 m and 5.52 m, the predicted results generally agree with the measured data. However, the simulations clearly illustrate the inherent core-annular pattern of the solids ﬂow. That is the particle concentrations are low in the center and high near the walls. Fig. 4 shows the computed and measured radial distribution of axial solids velocities. The simulation results show a similar distribution which generally ﬁts with the experimental results although the simulated velocities were slightly underpredicted at the upper section of the riser. In addition, the velocity proﬁles in the upper section are smoother than at the low region which is also captured

in the simulation, this phenomena might be due to the retardation in the core velocity. 4.1.2. Validation for coupled DLCFB model During the DLCFB experiment, a certain amount of the particles were present between the two reactors, so the initial inventory used in the simulations was calculated from the pressure drop between the reactor bottom and top from the experimental data. Figs. 5 and 6 display the predicted axial proﬁle of the pressure compare with the experimental measurement in the FR and AR, respectively. Two different operating gas velocities (a) vg,AR = 2.1 m/s, vg,FR = 1.8 m/s and (b) vg,AR = 2.6 m/s, vg,FR = 3.2 m/s were applied when validating the model. It can be seen that very good

8 7

Average mass flow [kg/s]

of the two systems are summarized in Tables 2 and 3, respectively. Other relevant simulation parameters are listed in Table 4. The simulations were run for 30 s of real simulation time and the time average was taken in the period from 10 s to 30 s.

Fuel reactor outlet Air reactor outlet

UAR = 2.6 m/s

6 5 4 3 2 1 0 1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

Gas superficial velocity of FR (UFR) [m/s] Fig. 10. Effect of superﬁcial gas velocity in FR on the averaged mass ﬂow at outlets of reactors.

Y. Zhang et al. / Powder Technology 310 (2017) 35–45

43

5

5

TSI = 37 kg TSI = 73 kg TSI = 109 kg TSI = 146 kg

4.5

Air Reactor

4

Fuel Reactor

4

TSI = 37 kg TSI = 73 kg TSI = 109 kg TSI = 146 kg

4.5

3.5

3.5

Superficial velocity

3

Reactor height [m]

Reactor height [m]

Superficial velocity FR: 1.8 m/s AR: 2.1 m/s

2.5

2

FR: 1.8 m/s AR: 2.1 m/s

2.5

2

1.5

1.5 Zoom in

1

1

0.5

0.5

0

3

0

0.05

0.1

0.15

0.2

0.25

0.3

Solid volume fraction [−]

(a)

0

0

0.05

0.1

0.15

0.2

0.25

0.3

Solid volume fraction [−]

(b)

Fig. 11. Effect of TSI on the solid volume fraction along the height of reactors.

agreement was achieved for both reactors and only minor discrepancies occurred in the lower regions of the reactors, close to the inlets. The simulations were not expected to do well in these regions for two reasons. One reason for the deviations may be the simpliﬁed gas distribution used at the inlet, which is not strictly consist with the experiment. Besides, the simpliﬁed cylindrical shape of the bottom of the reactors may be another contributor to the difference. In general, the comparison between calculated results and the experimental data indicating the interconnected method used in this work is applicable for predicting the performance of DLCFB reactor system.

4.2. Flow characteristics in the DLCFB A reference case is simulated in this section. The superﬁcial velocity of the FR and AR are 2.6 m/s and 2.4 m/s, respectively. Flow characteristics of the DLCFB reactor system including the solid concentration distribution and velocity distribution are examined. The solid volume fraction proﬁle of the DLCFB along the reactors height is illustrated in Fig. 7. The dense and dilute regions can be observed. The solids accumulate in the bottom of the reactors and the solid volume fraction proﬁle decrease exponentially along the height until the proﬁle is reaching a constant value at the upper parts, below 2%. So from this ﬁgure, it can be seen that both reactors are operated in the transition ﬂow regime between the fast ﬂuidization and the turbulent regime. Fig. 8 shows the time-averaged radial proﬁles of solids volume fraction and axial velocity at different axial position above the entrance. A typical core-annulus particle distribution was established at different axial positions. The solids mainly accumulate and move downwards at the walls, whereas a dilute gas-solid stream ﬂows upwards in the core of the riser. The ﬂows are fully developed in the upper section of the reactors. Since both reactors are operating in the same ﬂuidization regime, similar trends can be observed in both the FR and the AR. The radial solid distribution in the AR is more ﬂat in the core region compared to the distribution in the FR, which is because the diameter of the AR is larger than the FR.

4.3. Effect of gas superﬁcial velocity The gas superﬁcial velocity is crucial for the gas-solid interaction and the solid exchange between the FR and the AR. An issue which is challenging in the chemical looping combustion is the maximization of the fuel conversion. The oxygen carrier oxidation has always been an easy task because of the faster oxidation kinetics in the AR than the reduction kinetics in the FR ﬁnalizing the fuel conversion. For this reason, the AR operation was kept the same and not changed whereas several superﬁcial gas velocities of the FR were used to investigate the effect of increasing the FR gas velocity. The effect of changes in the FR velocity on the solid concentration proﬁle is shown in Fig. 9. As expected the increment in fuel reactor velocity caused lower solid concentration in the bottom region and higher solid concentration in the upper zone, which is due to the increased drag force with the increasing superﬁcial velocity. In the AR, the solid concentration is not sensitive to the gas velocity in FR since the inlet gas velocity of the AR has maintained. The same phenomena also were observed in the experiments conducted by Bischi et al. [18]. Fig. 10 shows the averaged mass ﬂow at the outlet of the two reactors. It is seen that the solid outlet ﬂow in the FR raised, which is the consequence of a high concentration increase in the FR upper part. Whereas the values are almost constant in the AR. The amount of exchanged solid between the reactors is determined by the lower solid ﬂow rate. So in the current operating conditions, the increased gas velocity in the FR enhanced the solid exchanges between the reactors. However increasing the FR gas velocity has the drawback of reducing the FR residence time, which might results in lower conversion of fuel.

4.4. Effect of total solid inventory Another parameter which can be used to control the system performance is the total solid inventory (TSI). For this reason it is important to understand how the reactor system responds to TSI

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Y. Zhang et al. / Powder Technology 310 (2017) 35–45

6. Nomenclatures

2 1.8

Average mass flow [kg/s]

1.6

Fuel reactor outlet Air reactor outlet

Superficial velocity FR: 1.8 m/s AR: 2.1 m/s

1.4 1.2 1 0.8 0.6 0.4 0.2 0 20

40

60

80

100

120

140

160

Total solids inventory [kg] Fig. 12. Effect of TSI on the averaged mass ﬂow at outlets of reactors.

C Calibration parameter C1 , C2 , Cb , Cl Turbulence model parameter dp Particle diameter, m e Coeﬃcient of restitution FD Drag force, kg/m2 s2 g Gravity acceleration, m/s2 g0 Radial distribution function ¯¯I Unit tensor kg Gas turbulent kinetic energy, m2 /s2 k M Interfacial momentum transfer of phase k, kg/m2 s2 pk Pressure of phase k, Pa r Radial coordinate, m Re p Particle Reynolds number St Turbulent kinetic energy production, kg/m2 s2 t Time, s U Superﬁcial gas velocity, m/s v k Velocity of phase k, m/s z Axial position above the inlet, m Greek letters

variations. The same ﬂuidization conditions were tested with four different inventories. The variation of the axial solid volume fraction proﬁles with the TSI are shown in Fig. 11. The increased solid mainly accumulated in the lower part. The inﬂection point from dense region to dilute region is affected signiﬁcantly by the TSI. When increasing the TSI, the inﬂection point will move upward. However the solid concentration is almost constant in the upper part, which results the averaged mass ﬂow at the outlet are not sensitive to the increasing TSI, as shown in Fig. 12. In addition, the ﬂows within the two reactors are operated in the transition regime between the fast ﬂuidization and the turbulent regime when the TSI is changed. Since the oxygen carriers are costly, further investigations are needed in order to optimise the amount of oxygen carrier required in the reactive system to maximum fuel conversion while minimizing the TSI.

Superscripts dilute max

Dilute Maximum

Subscripts

5. Conclusion A two-ﬂuid model with a kinetic theory of granular ﬂow closure was developed to predict the behaviour of an interconnected DLCFB which can be applied to the CLC system. The conﬁguration of the system consists of two reactors, the air reactor and the fuel reactor. Both reactors are operating in the fast ﬂuidization regime. The model simulates each reactor separately and connect the two reactors through speciﬁc boundary conditions, in which the solid ﬂow at the inlet of one reactor was set equal to the solid outlet ﬂow of the other reactor. First, the model was validated against the experimental data obtained from a DLCFB system and a CFB system published in [18] and [33], respectively. The predicted results show good agreement with the measured data as well as the typical coreannulus ﬂow characteristics of the riser can be observed, so the model is found to be applicable for predicting the performance of the system. The effects of operating conditions have been investigated. When increasing the FR superﬁcial gas velocity, more particles in the FR were entrained into the upper part of reactor which result in an increase in the outlet mass ﬂow, indicating that the solid exchanged between the reactors was enhanced. When the total solid inventory was increased, the additional particles are more likely to accumulate at the bottom of both reactors. The model is suﬃcient for cold ﬂow simulations. Further work continues to implement the reactive CLC system.

Volume fraction of phase k Interfacial drag coeﬃcient Collisional energy dissipation, kg/m3 s Turbulent energy dissipation rate, m2 /s3 Conductivity of granular temperature, kW/mK Viscosity of phase k, Pa • s Density of phase k, kg/m3 Stress tensor of phase k, Pa Turbulent stress tensor, Pa Granular temperature, m2 /s2

ak b cs eg js lk qk t¯¯ k t¯¯ t H

AR B FR g s t

Air reactor Bulk Fuel reactor Gas phase Solid phase Turbulent

Acknowledgments This work is part of the BIGCLC project supported by the Research Council of Norway (224866) and the BIGCCS Centre, performed under the Norwegian research program Centres for Environmentfriendly Energy Research (FME). The authors acknowledge the following partners for their contributions: Gassco, Shell, Statoil, TOTAL, ENGIEand the Research Council of Norway (193816/S60).

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